The Icahn School of Medicine at Mt. Sinai offers an early assurance program called FlexMed for sophomores on the premedical track. Students can only apply in their sophomore year and if accepted, will matriculate into Mt. Sinai's medical school upon graduation. Here are the program description and admission requirements. The program is open to all undergraduate sophomores regardless of their major.
The deadline to apply for this year's program is January 15, 2016.